ShadowClock

How ShadowClock works

A vertical object of height H casts a shadow of length L on level ground. The Sun's elevation is then h = atan(H / L), and it stands opposite the shadow's direction. ShadowClock searches for every instant (or place) where the Sun was at that position, using the NREL Solar Position Algorithm.

Find the time

1. Enter the place, and how precisely you know it.
2. Measure one or more shadows. Add a second object in the same photo, or another photo of the same place with its time offset (EXIF differences are usually exact even when the camera clock is wrong).
3. Narrow the search with what you know: years, months, time of day.

Find the place

Give each shadow the UTC time it was taken. One shadow places you on a ring around the point where the Sun was overhead; each extra shadow at another time adds a ring, and the rings cross at the answer.

Reading the results honestly

• Twice a year: the Sun follows almost the same path on two dates placed symmetrically around a solstice, so a shadow usually matches two periods per year. Near a solstice they merge into one wide period.
• No year: the Sun's path repeats every year. Shadows cannot tell years apart.
• Uncertainty: ± values are one standard deviation (Gaussian); min–max values are hard bounds. The penumbra (the Sun is 0.53° wide), tilt of the object and refraction are included. 68 / 95 / 99.7 % regions follow the χ² distribution of the combined shadows.
• Probabilities compare the solutions assuming every allowed instant was equally likely beforehand.

Assumptions

• The object is vertical (within the tilt you give) and the ground is flat and level where the shadow falls.
• Lengths and directions are measured in the real scene or on a rectified image — perspective in a raw photo distorts both.
• Azimuths are relative to true north; convert compass readings with the local magnetic declination.